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Higher rank
quantum-classical correspondence
Joachim Hilgert, Tobias Weich and Lasse L. Wolf |
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Vol. 16 (2023), No. 10, 2241–2265
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Abstract |
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For a compact Riemannian locally symmetric space of arbitrary rank we determine the location of certain Ruelle–Taylor resonances for the Weyl chamber action. We provide a Weyl-lower bound on an appropriate counting function for the Ruelle–Taylor resonances and establish a spectral gap which is uniform in if is irreducible of higher rank. This is achieved by proving a quantum-classical correspondence, i.e., a one-to-one correspondence between horocyclically invariant Ruelle–Taylor resonant states and joint eigenfunctions of the algebra of invariant differential operators on . |
Keywords
compact locally symmetric space, Poisson transform,
spectral correspondence, Weyl chamber flow
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Mathematical Subject Classification
Primary: 22E46, 37C85, 37D20, 43A90, 58J50
Secondary: 58J40
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Milestones
Received: 16 March 2021
Revised: 7 March 2022
Accepted: 28 May 2022
Published: 11 December 2023
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Authors |
| Joachim Hilgert | |
| Institut für Mathematik Universität Paderborn Paderborn Germany |
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| Tobias Weich | |
| Institut für Mathematik Universität Paderborn Paderborn Germany |
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| Lasse L. Wolf | |
| Institut für Mathematik Universität Paderborn Paderborn Germany |
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| © 2023 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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